New results on high-order risk changes

作者：Menegatti Mario^*

来源：European Journal of Operational Research, 2015, 243(2): 678-681.

DOI：10.1016/j.ejor.2014.12.023

• Utility theory
• Risk
• nth-Order risk change
• nth-Order derivatives

This note extends the results on the first four derivatives of the utility function by Menegatti (Eur. J. Oper. Res. 232 (2014) 613-617) to the case of high-order derivatives. We show that, under usual assumptions, if the generic derivative of the utility function of order n is sign invariant then all the derivatives from order n to order 2 alternate in sign. We then focus on the case where the derivative of the utility function of order n is either positive when n is odd or negative when n is even, and we show the implications of this result for high-order risk changes and for saving decisions.

• 出版日期2015-6-1